Homework Help is Here – Start Your Trial Now!
Math
Statistics
Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with standard deviation 5. On which test did she do better relative to the rest of the class? statistics test b. psychology test c. the same d. cannot answer with given information (Ctrl) -

Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with standard deviation 5. On which test did she do better relative to the rest of the class? statistics test b. psychology test c. the same d. cannot answer with given information (Ctrl) -

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
See similar textbooks
icon
Related questions
Question
**Statistical Comparison of Test Scores** Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with a standard deviation of 5. On which test did she do better relative to the rest of the class? **Possible Answers:** - a. statistics test - b. psychology test - c. the same - d. cannot answer with given information **Explanation:** To determine on which test Samantha performed better relative to her classmates, we need to calculate her z-scores for both tests. The z-score tells us how many standard deviations away from the mean her score is. **For the Statistics Test:** - Score: 85 - Mean: 75 - Standard Deviation: 8 The z-score is calculated as follows: \[ z = \frac{(X - \mu)}{\sigma} \] \[ z = \frac{(85 - 75)}{8} \] \[ z = \frac{10}{8} \] \[ z = 1.25 \] **For the Psychology Test:** - Score: 72 - Mean: 60 - Standard Deviation: 5 The z-score is calculated as follows: \[ z = \frac{(X - \mu)}{\sigma} \] \[ z = \frac{(72 - 60)}{5} \] \[ z = \frac{12}{5} \] \[ z = 2.4 \] Samantha's z-score for the Psychology test (2.4) is higher than her z-score for the Statistics test (1.25), indicating that she performed better on the Psychology test relative to the rest of the class. Thus, the correct answer is: - b. psychology test
Transcribed Image Text:**Statistical Comparison of Test Scores** Samantha is taking Statistics and Psychology classes during this summer session. She received a score of 85 on her Statistics test for which the class mean was 75 with a standard deviation of 8. She received a score of 72 on her Psychology test for which the class mean was 60 with a standard deviation of 5. On which test did she do better relative to the rest of the class? **Possible Answers:** - a. statistics test - b. psychology test - c. the same - d. cannot answer with given information **Explanation:** To determine on which test Samantha performed better relative to her classmates, we need to calculate her z-scores for both tests. The z-score tells us how many standard deviations away from the mean her score is. **For the Statistics Test:** - Score: 85 - Mean: 75 - Standard Deviation: 8 The z-score is calculated as follows: \[ z = \frac{(X - \mu)}{\sigma} \] \[ z = \frac{(85 - 75)}{8} \] \[ z = \frac{10}{8} \] \[ z = 1.25 \] **For the Psychology Test:** - Score: 72 - Mean: 60 - Standard Deviation: 5 The z-score is calculated as follows: \[ z = \frac{(X - \mu)}{\sigma} \] \[ z = \frac{(72 - 60)}{5} \] \[ z = \frac{12}{5} \] \[ z = 2.4 \] Samantha's z-score for the Psychology test (2.4) is higher than her z-score for the Statistics test (1.25), indicating that she performed better on the Psychology test relative to the rest of the class. Thus, the correct answer is: - b. psychology test
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
SEE MORE TEXTBOOKS